Method of designing orthogonal filters

ABSTRACT

A method of designing an orthogonal filter for use in a speech synthesizing system wherein the filter is constructed from a series of linear filter sections. The poles in the complex plane of any section of the filter are cancelled by the zeros of the next section.

O United States Patent H 1 1 3,800,093

Wolf Mar. 26, 1974 METHOD OF DESIGNING ORTHOGONAL FILTERS I PrimaryExaminerl(athleen H. Claffy Assistant Examiner-David L. Stewart [76]Inventor' g ifggg zg BOX Attorney, Agent, or Firm-R. S. Sciascia; Q. E.Hodges 221 Filed: on. 20, 1971 5 ABSTRACT [21] Appl. No.: 191,003 Amethod of designing an orthogonal filter for use in a speechsynthesizing system wherein the filter is constructed from a series oflinear filter sections. The 179/15 179/1555 poles in the complex planeof any section of the filter 58] Fie'ld 55 15 B0 are cancelled bythezeros of the next section.

333/20, 70 R 4 Claims, 5 Drawing Figures MULTIPLIER vTlME-f SPEECHSIGNAL T PORAL Q' (SAMPLE LENGTH T q I 4 o T MULTIPLIER fiTlME-tTEMPORAL on Q G AVERAGER 2 MULTIPLIER TEMPORAL a AVERAGER n Io I2 M. I 0TIME t WHITE NOlSE 9(1) ORTHOGONAL SOURCE v FILTER IsPEcTRA H (S)DENSITY N) I FIRST SECTION HHS) -42 v m 4s v u) .o l sz I SUBSEQUENTSECTIONS FIG. 3.

62 If H 64 6O INPUT I oOUTPUT F/ INVENTOR.

ALFRED A. WOLF A r TORNE Y PAIENTEIJIIIII26 I974 3800.093

SHEET I 0F 4 GAUSSIAN -20 WHITE NOISE SOURCE (SPECTRAL. DENSITY l/NORTHOGONAL W (I) FILTER w I H (S) 24 MULTIPLIER EXTRACTION 0 J"COEFFICIENTS MULTIPLIER 30 I I A h 2 RECONSTRUCTED FIG 5 SPEECH SIGNALINVENTOR.

ALFRED A. WOLF AT IVE) 1 METHOD or DESIGNING onrnoconAr. FILTERS Thisapplication is a continuation-in-part of an application filed on June23, 1971 bearing the Ser. No. 155,988 now US Pat. No. 3,746,791, issuedJuly 17,

The invention described herein may be manufactured and used by or forthe Government of the United States of America for governmental purposeswithout the payment of any royalties thereon or therefor.

FIELD OF INVENTION An orthogonal filter is a filter whose output is aset of orthogonal functions related by their coefficients to the inputsignal to said filter. If the input signal is random white noise, thenthe filters output is a set of random orthogonal functions. If thecoefficients for this set of random functions are properly selected, anyvoice signal may be reproduced by temporally averaging the resulting setof orthogonal functions.

With the advent of systems in which there is a man/- machine interfacesuch as computer systems or control systems, it is desirable for a manto be able to communicate with the machine as easily as possible. Theideal situation would be to have the man speak to the ma- DESCRIPTION OFTHE PRIOR ART In the prior art there is no known general method ofdesigning an orthogonal filter. The US. Pat. to Norbert Wiener, Nos.2,024,900 and 2,128,257 describe the design of a specific orthogonalfilter which was empirically developed for his situation. Thisorthogonal filter was the only known orthogonal filter from the date ofthe Wiener patents to the present time. The present method was developedwhile designing an orthogonal filter for use in a speech synthesizingsystem and the method is most clearly described in combination with thespeech system.

One of the most popular man/machine interface schemes in which the manmerely talks to a machine employs the fact that in each languagethereare a few basic sounds-that make up the words in that language.These basic sounds are called phonemes. ln more precise language,phonemes are the sound features which are common to all speakers of agiven speech form and which are exactly reproduced in repetition. In anylanguage there are a definite and small number of phonemes. 1n theEnglish language there are 46 phonemes. These phonemes are knownsoundwise, and any system employing phonemes records the basic phonemesounds on magnetic tape or some other recording means. A computerprogram is then written to connect the proper phonemes to produce wordsthat convey speech information in the form of recurrent patterns. Insuch a system one can type information into, say a computer, and have itspeak back to the operator.

To date such systems have the disadvantage that, as the vocabulary ofthe system increases the computer programs become more complicated. Thusthe speech vocabulary of such systems is usually very limited. Anotherdisadvantage of the system is that the words spoken by the computer aregenerally of poor fidelity and difficult to understand. Also, such asystem is not flexible since the information that can be conveyed by thecomputer depends on the extent of the vocabulary of the computer, thatis, the complexity of the computer program.

Another type of speech synthesizer system is known as the Vocoder (VoiceCoder). The Vocoder dates back to the l920s. The standard Vocoder is aspectrum/channel vocoder. It consists of an analyzer which produces asignal proportional to the short term amplitude spectrum of thefundamental frequency of the speech input, and the synthesizer consistsof devices that reconstruct speech by means of electrical signalsappearing at the analyzer output. In both the analyzer and thesynthesizer, signals are generated that are proportional to both thevoiced and unvoiced sounds and the pitch of the sounds. There are, ofcourse, other speech analyzer/synthesizer systems which will not bedealt with here.

Suffice it to say that in each of these systems the method of speechused by the human is imitated in one way or another or the linguisticproperties of speech are capitalized upon.

It is'an object of the present disclosure to provide a a general methodof designing orthogonal filters.

It is another object of the present disclosure to provide an orthogonalfilter for use in a speech synthesizing system.

' These and other objects of the present invention are set forth in thefollowing disclosure.

SUMMARY OF THE INVENTION The present speech system capitalizes on thefact that speech is a stochastic process. Speech is stochastic becauselong samples of speech convey information which is probabilistic intime. The present system employs a gaussian white noise source; theoutput of which is passed through an orthogonal filter to produce a setof random orthogonal functions which when multiplied by a speech signaland averaged produces coefficients which can be used to synthesizespeech information at a later time. This method is somewhat analogous tothe use of generalized Fourier coefficients to define and reproduce aperiodic function.

DESCRIPTION OF THE DRAWINGS DESCRIPTION OF THE PREFERRED EMBODIMENTS Thepresent invention relates to a general method for designing orthogonalfilters. In particular an orthogonal filter design is disclosed whichmay be used in a speech synthesizing and codifying system.

It should be noted that the following mathematical terminology isstandard in the art and can be found in the textbook'published by theAddison-Wesley Publishing Company, entitled: Principles of FeedbackControl," written by Charles H. Wilts, as well as other textbooks.

This invention makes it possible to transform a sample of speech oflength, T into a set of speech coefficients designated by a a a,,, eachof which depends on time according to the sample length, T of the speechsample, which is explained further below. These coefficients a a n canbe thought of as a set of generalized Fourier coefficients defined on aset of orthogonal noise sample functions obtained from a white noisesource. If the waveform of the speech sample, of length T is denoted byx(t), then by making use of the fact that x(t) is a sample function froma stochastic process, it can be decomposed into an infinite series oforthogonal sample functions taken from a white noise source. Eachorthogonal sample function is weighted by a coefficient the value ofwhich depends on the speech sample under consideration. The set ofcoefficients (a n l, 2, thus contains the necessary information fromwhich the original speech sample can be reconstructed by weighting theorthogonal sample functions {w,. (t): n 1,2,. (see FIG. 5) withtheappropriate corresponding coefficient, a,,: n l, 2, in which T is astrip of time running to infinity and r is a given instant of time. Theinvention makes possible the maximum compression of speech by using thecoefficients am l, 2, l to convey information. Using these coefficients,it is now possible for man to communicate with computers and to havethem in turn communicate with man by means of speech. This inventionopens up the possibility of new, unforeseen innovations in machines andsystems in which'there is a speech communication interface with man.-One such example, in addition to the possibility of talking to acomputer is the possibility of talking to a typewriter.

DESCRIPTION OF THE COEFFICIENT OR CODING GENERATOR FIG. 1 is a blockdiagram of the system for obtaining the speech extraction coefficients:The speech signal 2, denoted by the sample functions x(t) of samplelength T is multiplied (instant by instant) by each orthogonal noisesignal denoted respectively by the sample functions v (r), v (t), v (t),v,,(t), which are derived as the set of outputs of an orthogonal filter12, described below when the white noise signal 10, denoted by thesample functioni g(t)}, of spectral density N watts per cycle, isapplied to the orthogonal filters input. The sample functions thatresult from the multiplication of the set of orthogonal noise samplefunctions v,(t), v,,(t) with the sample function x(t) in the multipliers4, 6, and 8, are the speech extraction samples of length T seconds asdenoted by v,,(t) x(t): n l, 2, This set of product sample functionsv,(t) x(t), v,(t) x(t), v (t) x(t), v,,(t) x(t) is averaged temporallyin the temporal averages l4, l6, and 18 give rise to the correspondingset of cofficients. a a a a,,, where mathematically these averages areformally given by the equations:

1 T a3= J v (t)x(t)dt (3) CW where Tis the averaging time and is atleast equal to the sample length, T of the speech sample. The integralover (0,?) of each of the product sample functions, v,,x divided by T isthe temporal average of those sample functions. The resulting speechextraction coefficients a,, a a, are dependent only on the samplelength, T and are the coefficients that represent the essentialinformation needed to reconstruct the speech signal, x(t). A rule ofthumb for the value of T, the averaging time is that about ten times thesample length, T o of the speech sample.

GENERATION OF THE ORTl-IOGONAL NOISE FUNCTIONS In the generation of thespeech code, a,, a a a,,, it is necessary to generate a correspondingset of random sample functions v,(t), v (t), v (t), v,,(t), that arepairwise orthogonal. By pairwise orthogonality we roughly mean that theinformation contained in each of the sample functions v (r), v,(t),v,,(t) is unique. To put this another'way, no overlap in informationexists between any two sample functions v,(t), v,(z), v,,(z). Fordescriptive purposes, the generation of the orthogonal random samplefunctions is achieved by means of an orthogonal filter when whitenoiseof power spectral density N is applied to the input of the orthogonalfilter.

The orthogonal filter is a linear filter with one pair of inputterminals and many pairs of output terminals. The filter, which isdescribed below in detail, may be roughly likened to an ideal prism onwhich white light is incident. The incident light may be thought of asthe input to the prism. The output of an ideal prism is essentially thecomplementary colors in response to the incident white light upon it.The complementary colors are of course pairwise orthogonal. In our case,however, the orthogonal functions are random within a band offrequencies whereas in the prism case the complementary functions are inprinciple roughly single frequency sinusoids with random amplitudes andrandom phases. The latter is due to the randomness of the white light.

CONSTRUCTION OF THE ORTHOGONAL FILTERS Linear orthogonal filters can beconstructed as a chain of linear filter sections in which the poles ofany section of the filter, in the complex plane, is essentiallycancelled by the zeros of the next immediate section. FIG.-2 shows thisgeneral scheme for constructing an orthogonal filter. The complexfunction H,(s) is the transfer function of the first section of thefilter as a funst netw qe e z fr=q ns ar bl i w ch a jw s where .f=FEQP'F"?! i eye et per. sec nd n-th output terminal pair of theorthogonalfilter. The process for realizing the actual construction ofan orthogonal filter is given by the following formula:

Let I-I,(s) be the transfer function of the first filter section. ThenThe numerator B(s) is selected to satisfy the equation and thedenominator C(s) is selected to satisfy the equation C (s) c c s c s"(8) where the constants b b b and the constants c c c are chosen suchthat H(s) is physically realizable. In a like way the transfer functionis designed such that the numerator C (s) is exactly like thedenominator of the first section, H,(s) with s replaced by (s). Thismakes the zeros of H (s) H (s)H (s) occupy the same positions as thepoles of H,(s) except that they are reflected about the jw-axis. Hence,the zeros of one transfer functio in effect cancel the poles of the nextsection giving rise to the orthogonality of the pair. In general, then-th transfer function of the orthogonal filter from the input of thefilter is given by the formula ff cn- H,.(s) KnBts) (1 H k( n for n s 2.Where the symbol, H is the product of all is the product of all factorsin the expansion of Equation 10 from I to n. For this speech device, afilter is developed using this process of construction of orthogonalfilters having simple poles and zeros along the axis of the reals. Thisgives rise to simple resistancecapacitance (RC) network withdifferential amplifiers. The RC orthogonal filter is shown in FIG. 3.The first section of the filter includes an input resistor 34, feedbackresistor 36 designated as R in Equation 13, feedback capacitor 38,designated as C in Equation 13, and operational amplifier 40. Thesubsequent section of the filter includes inputs resistors 42, 44,designated as r and r in Equation 15 respectively, resistors 48, 50, 54,and 56; capacitors 46, 52; and differential amplifier 58. Resistors 48and 50 are designated as R, in Equation 17, resistors 54 and 56 aredesignated as R and R respectively in Equation 16 and capacitors 46 and52 are designated as C, in Equation 17. For these filters the transferfunction of the first section is given by i/ 1) (It) and for n a 2 A n/n) n-1/ n) n-m) where for design purposes the first pole is placed at salong the real axis where and sec-

. are placed according to the n/ IP!) m m) In the ordinary orthogonalfilter, the poles s s s can be placed arbitrarily along the real axis.But for the speech synthesizer this procedure will fail to work. It isimportant to place the poles s s s in such way as to make thereconstructed signal converge to the desired speech signal. In theprocess of constructing an orthogonal filter for the speech synthesizerthe first pole is selected approximately equal to the bandwidth of thespeech signal. Since speech signals can cover a bandwidth of the orderof 200 Hz to 2,500 Hz, depend-- ing on the speaker, s, can be selectedto be a frequency within this range. To make the reconstructed signalconverge to the original speech signal in the mean squared sense, theremaining poles are chosen according to the formula s s /n n 2 1 18) Ifthe remaining poles are placed according to the formula s" lln n 2 1(1.9) then the reconstructed signal will converge absolutely almosteverywhere. In general be needed for convergence. There is a practicaldifficulty however, which causes a resolution problem in placing thepoles at distinct positions along the real axis.

SUMMARY OF THE GENERAL PROCESS FOR PRODUCING ORTHOGONAL FILTERS 1.Select the nature of the poles of the orthogonal filter to be, i.e.,whether they are simple or complex, from the application for which thefilters are to be .us d- I log Hn(w) dw 1 m is satisfied where: H,,(w)|H,,(jw)| is the amplitude characteristic of the transfer functionH,,(s).

4. From each transfer function, i.e., H,(s) and H (s),

etc. given by and (23) where etc. the circuit is synthesized accordingto standard procedure noting that the placement of the poles must followthe requirements of convergence if forexample a speech signal is to bereconstructed.

5. Once a design of H,(s) and H (s) are made, the orthogonal filter ismade by cascading H (s) and H (s) together and then adding to thiscascade as many sections as needed according to the requirements of theapplication, in which subsequent sec tions are identical to H (s) interms of the circuit used. c

The individual sections following the second section are designedaccording to the formula It is therefore clear that in terms of thecircuit all the H (s) for n 2' 2 are the same with the exception of thecircuit parameters which depend only on n, the number of the section.Hence, the additional requirements on the poles depend on theconvergence of the reconstruction process or on some other physicalrequirement. The resulting chain is now an orthogonal filter.

6. The design of the transfer functions H,(s), H (s), H (s), depend onthe placementof the poles- 0 s s s These in turn define the constants b5 S S /n c. For convergence almost everywhere S S1/n d. For other typesof convergence S, S /n;p 4

7. The kind of convergence or the method of pole placement dependson theapplication intended 5 note by the symbols {w (t):K=1, 2,

and once that is decided, the resolution of pole placement is determinedand the resulting error in convergence can be estimated.

8. Once the transfer function is designed according to the process givenin steps I through 7 above, the hardware is obtained by standard analogcomputer techniques or by factoring the transfer functions and thendetermining the equivalent partial fraction expansion using amplifiersand differential amplifiers to take account of the negative signs thatmay result from the partial fraction constants. The process describedabove is the one used to obtain the hardware configuration of theorthogonal filter shown in FIG. 3.

SIGNAL MULTIPLIERS The signal multipliers shown in FIG. 1 formultiplying the orthogonal noise components of the white noise sourcewith the speech signal are standard devices. In the frequency range ofinterest, i.e., bandwidths up to 20 KHz, the quarter Gauss square methodwas used. Other types can easily be used instead.

The quarter Gauss square multiplier is one that makes use of theidentity (A+B) (A-B) 4 AB TEMPORAL AVERAGER The temporal averager is asimple RC low pass filter with a very long time constant compared to thehighest frequency component in the speech signal. If f denotes thisfrequency, then FIG. 4 gives an example of the configuration of thetemporal averager. The temporal averager consists of input resistor 60,feedback capacitor 62 and amplifier 64.

GAUSSIAN WHITE NOISE SOURCE The Gaussian white noise source is astandard noise generator of the diode type.

SYSTEM FOR THE RECONSTRUCTION OF THE SPEECH SIGNAL FROM SPEECHEXTRACTION COEFFICIENTS AND WHITE NOISE Once the speech extractioncoefficients, a a,, a a, are obtained from the Speech Extraction CodeGenerator, shown in FIG. I, it is possible to reconstruct from thesecoefficients the original'speech sample, x(t). The reconstruction ofx(t) is carried out by multiplying each coefficienfl a :k= l, 2, n} by acorresponding set of orthogonal noise functions which we shall den and 0st and then summing the resulting set of products.

Thus, we form the set of products a1 w (t), a w (t),

a w (t), a,.wn(t) and then sum to obtain the reconstructed speech signalx(z) as the summation Sn z i at-wkm (2 It is evident by analogy that thecoefficients a a a correspond to the coefficients of a Fourier seriesand the orthogonal noise functions w (t), w (t), w (t),- w,,(t)correspond to the orthogonal set of trigonometric functions. Equation27) is the partial sum of a generalized random orthogonal series whichconverges as n to the speech sample x(t) in some probabiliscan becalculated from the equation For a speech sample x will be fixed. Then 6is smallest when is largest.

THE PHYSICAL RECONSTRUCTION SYSTEM FIG. is a block diagram of the speechreconstruction system. Using the coding coefficients 21,, a a and aGaussian white noise source of spectral power density of l /N watts percycle the speech sample function, x(t) is reconstructed according to thedescription given above.

In FIG. 5, the white noise signal, k(t) of spectral density of l/N wattsper cycle is applied to an orthogonal filter which has a transferfunction, H,,(s) identical to the orthogonal filter of the codinggenerator shown in FIG. 1. The response of this orthogonal filter is theset of orthogonal noise sample functions w,(t), w (t), w (t), w,,(t).Each of these is multiplied respectively by the coefficients a,, a aderived from the coding generator (FIG. 1). The products thus formed ineach of the multipliers is summed in the adder to give x(t) e Ewe) (29)k= l v V It will be noted that the elements of the reconstruction systemare quite similar to the coefficient code generator system. Theorthogonal filter is the exact same design as in the code generatorcase. The white noise source of the reconstruction system differsfromthe coding generator system in that the spectral density of one is thereciprocal of the other.

The multiplier is a signal multiplier the same as described previouslyabove. The speech extraction coefficients can be stored in a memory suchas a tape as voltages of appropriate value.

THE ADDER The summing of the products a w (t), a w (t), a,,w,,(t) areaccomplished in a conventional adder.

RELATIONS BETWEEN SPECTRAL DENSITIES Since the white noise source of thegeneration and .reconstruction systems have reciprocal spectral densityfunctions, the sample functions are related according t0 El!) Wu 4 92SUMMARY In the method presented here the speech analysis and synthesistechnique capitalizes onthe factthat speech-- I is a random signal thatcan be decomposed into a generalized orthogonal series something likethe Fourier series. This means that a speech signal can be representedby a set of coefficients which depend only on the nature of the speechinformation and on the length of the speech sample. This speechsynthesizing system is an electronic system for accomplishing thegeneration of these speech coefficients or speech extraction parametersand for utilizing them to reconstruct the speech into a spoken signal.

The novelty of the system consists in the utilization of orthogonalfilters, white noise and temporal averaging devices connected in theunique arrangement shown in FIG. ll that gives rise to the speechextraction coefficients, a a a It should be noted that the speechextraction parameters are very narrow band signals. These signals arenearly constant for T T,,. This also means that the system can be usedto greatly compress speech.

Obviously many modifications and variations of the present invention arepossible in the light of the above teachings. It is therefore to beunderstood that withing the scope of the appended claims the inventionmay be.

practiced otherwise than as specifically described.

What is claimed is: l. A method for making an orthogonal filter havingsections 1 through n comprising the steps of:

selecting a first transfer function as wherein the numerator B(s) isselected to satisfy the relationship:

and the denominator C is selected to satisfy the following relationship:

C18) C10 C S C S'" wherein the constants b,,, b b and the constants c cc are chosen such that H (.r) is capable of being manufactured fromrealizable components;

constructing a first filter section having as its transfer function saidfirst transfer function; placing said first filter section firstserially in a group of n filter sections; select ng a sspn ansfe funstszn V electing the numerator of the second equation C,(s) and thedenominator of the first equation C (s) of the transfer function so thatthe zeros of the second transfer function occupy the positions of thepoles of the first transfer function and are reflected about thejcu-axis, and with the effect that poles of the first transfer functioncancel the zeros of the second transfer function thereby producingorthogonality; constructing a second filter section having as itstransfer function said second transfer function; placing said secondfilter section second serially after said first filter section in agroup of n filter sections;

arranging each successive section following section 2 such that thezeros of their respective tmsfer functions occupy the positions of thepoles of the preceeding transfer functions reflected about the jw axisand with the zeros of the successive transfer t nsti n .ssn sllis thepoles OM19- arsss s as transfer function thereby giving rise toorthogonality; and,

arranging the n-th successive filter section of the orthogonal filtersuch that the transfer function of each filter in a series including nfilters is described by the relationship:

11:11 Ck(s) Hits) KnBm H C (s) K=l wherein k signifies all the filtersin the series from the first filter to the n-th filter, inclusively.

2. A method as defined in claim 1 wherein the orthogonal filter is to beused in a speech synthesizer including the steps of:

selecting s, to be within the frequency range of 200 Hertz to 2,500Hertz, and

selecting the remaining poles in accordance with the formula wherein theconstants b,,, b,, .b and the constant c c .0 are chosen such that H (s)is capable of being manufactured from realizable components;

a second section characterized by the transfer function z( z/ i) 1 ("U/2 wherein the numerator of the second equation C,(s)

and the denominator of the first equation C,(s) of the transfer functionare selected such that the zeros of the second transfer function occupythe positions of the 5 poles of the first transfer function and arereflected about the jw-axis, and with the effect that poles of the firsttransfer function cancel the zeros of the second transfer functionthereby producing. orthogonality;

arranging each successive filter section following section 2 such thatthe zeros their respective transfer function occupy the positions of thepoles of the preceeding transfer function reflected about the jw axisand with the zeros of the transfer function of the successive filtersection cancelling the poles of the transfer function of the preceedingsection thereby giving rise to orthogonality; and

e r w s a sriaspy the rwsfsrfunstisan wherein k denotes all the filtersections in the series from the first filter to the n-th filterinclusive.

4. An orthogonal filter as defined in claim 3 for use in a speechsynthesizing system which further includes: selecting s, from within therange of 200 Hertz to 2,500 Hertz, and selecting the remaining poles inaccordance with the formula n =(s /n for n 2 l. l

1. A method for making an orthogonal filter having sections 1 through ncomprising the steps of: selecting a first transfer function as H1(s)K1(B(s)/C1(s)) wherein the numerator B(s) is selected to satisfy therelationship: B(s) bo + b1s + . . . bksk and the denominator C1 isselected to satisfy the following relationship: C1(s) c10 + c11s + . .. + c1msm wherein the constants bo, b1, . . ., bk and the constants c10,c11, . . ., c1m are chosen such that H1(s) is capable of beingmanufactured from realizable components; constructing a first filtersection having as its transfer function said first transfer function;placing said first filter section first serially in a group of n filtersections; selecting a second transfer function as H2o(s) (K2/K1)(C1(s)/C2(s)) electing the numerator of the second equation C1(-s) andthe denominator of the first equation C1(s) of the transfer function sothat the zeros of the second transfer function occupy the positions ofthe poles of the first transfer function and are reflected about the jomega -axis, and with the effect that poles of the first transferfunction cancel the zeros of the second transfer functiOn therebyproducing orthogonality; constructing a second filter section having asits transfer function said second transfer function; placing said secondfilter section second serially after said first filter section in agroup of n filter sections; arranging each successive section followingsection 2 such that the zeros of their respective trnsfer functionsoccupy the positions of the poles of the preceeding transfer functionsreflected about the j omega axis and with the zeros of the successivetransfer function cancelling the poles of the preceeding transferfunction thereby giving rise to orthogonality; and, arranging the n-thsuccessive filter section of the orthogonal filter such that thetransfer function of each filter in a series including n filters isdescribed by the relationship:
 2. A method as defined in claim 1 whereinthe orthogonal filter is to be used in a speech synthesizer includingthe steps of: selecting s1 to be within the frequency range of 200 Hertzto 2, 500 Hertz, and selecting the remaining poles in accordance withthe formula sn (s1/n3) for n > or =
 1. 3. An orthogonal filter havingsections 1 through n comprising: a first section characterized by thetransfer function H1(s) K1(B(s)/C1(s)) wherein the numerator B(s) isselected to satisfy the relationship: B(s) bo + b1s + . . . + bksk andthe denominator C1 is selected to satisfy the following relationship:C1(s) c10 + c11s + . . . + c1msm wherein the constants bo, b1, . . .bkand the constant c10, c11, . . .c1m are chosen such that H1(s) iscapable of being manufactured from realizable components; a secondsection characterized by the transfer function H2o(s) (K2/K1) (C1(-s)/C2 (s)) wherein the numerator of the second equation C1(-s) and thedenominator of the first equation C1(s) of the transfer function areselected such that the zeros of the second transfer function occupy thepositions of the poles of the first transfer function and are reflectedabout the j omega -axis, and with the effect that poles of the firsttransfer function cancel the zeros of the second transfer functionthereby producing orthogonality; arranging each successive filtersection following section 2 such that the zeros their respectivetransfer function occupy the positions of the poles of the preceedingtransfer function reflected about the j omega axis and with the zeros ofthe transfer function of the successive filter section cancelling thepoles of the transfer function of the preceeding section thereby givingrise to orthogonality; and an n-th section characterized by the transferfunction
 4. An orthogonal filter as defined in claim 3 for use in aspeech synthesizing system which further includes: selecting s1 fromwithin the range of 200 Hertz to 2,500 Hertz, and selecting theremaining poles in accordance with the formula sn (s1/n3) for n > or =1.